This study uses datasets provided by three German leasing companies, which shall be referred to herein as companies A, B, and C. All three companies use a default definition consistent with the Basel II framework. According to Table 2.1, the dataset from lessor A contains 9,735 leasing contracts with 5,811 different customers and default dates between 2002 and 2010. The dataset from lessor B contains 2,995 leasing contracts with 2,344 different lessees who defaulted between 1994 and 2009, with the majority of defaults occurring between 2001 and 2008. The dataset for leasing company C consists of 1,592 leasing contracts with 864 different lessees who defaulted between 2002 and 2009.
For the defaulted contracts, we calculate the LGD as one minus the recovery rate. The recovery rate is the ratio of the present value of cash inflows after default to the exposure at default (EAD). For leasing contracts, the cash flows consist of the revenues obtained by redeploying the leased asset and other collat- eral combined with other returns and less workout expenses. The cash flows are discounted to the time of default using the term related refinancing interest rate.1
The EAD is the sum of the present value of the outstanding minimum lease pay- ments, compounded default lease payments, and the present residual value. All values refer to the time of default. A contract is classified as defaulted when at least one of the triggering events set out in the Basel II framework has occurred.
1Only a few studies (such as Gibilaro and Mattarocci (2007)) address risk-adjusted discounting.
We use the term related refinancing interest rate to discount cash flows at the time of default, independently of the time span of the workout and the risk of each type of cash flow.
2.2 Dataset 15
Before the data was collected, all three companies agreed to use identical defi- nitions for all the elements that are entered into the LGD calculation, and for all details of the leasing contract, lessee, and leased asset. Thus, for every contract, we have detailed information about the type and date of payments that the lessor received after the default event. Moreover, we incorporate expenses arising during the workout into the LGD calculation, to meet Basel II requirements. Workout costs are rarely considered in empirical studies.
The workouts have been completed for all the observed contracts. Gürtler and Hibbeln (2013) recommend restricting the observation period of recovery cash flows to avoid the under-representation of long workout processes, which might result in an underestimation of LGDs. Because we do not see a similar problem in our data, we do not truncate our observations based on that effect.
All three companies also provide a great deal of information about factors that might influence the LGD, which we divide into four categories:
1. contract information; 2. customer information; 3. object information; and
4. additional information at default.
Contract information is elementary information about the contract, such as its type, e. g., whether it was a full payment lease, partial amortization, or hire- purchase; its duration; its calculated residual value or prepayment rents; and in- formation about collateralization and/or purchase options. Customer information mainly identifies retail and non-retail customers. The category object information consists of basic information about the object of the lease, including its type, ini- tial value, and supplementary information, such as the asset depreciation range. Whereas all the information in the first three groups is available from the moment the contract is concluded, the last category consists of information that only be-
Company Mean Std P5 P25 Median P75 P95 A 0.52 0.40 −0.11 0.19 0.52 0.88 1.05 B 0.35 0.42 −0.18 0.00 0.25 0.72 1.01 C 0.39 0.42 −0.23 0.03 0.32 0.77 1.03
Table 2.2: Loss given default (LGD) density information for companies A–C. Std is the standard deviation and P5–P95 are the respective percentiles.
comes available after the contract has defaulted, such as the exposure at default and the contract age at default.
Descriptive statistics
The LGD is clearly not restricted to the interval [0,1]. As presented in Table 2.2 and Figure 2.1, negative LGDs are not only theoretically possible but also occur frequently in the leasing business. Hartmann-Wendels and Honal (2010) argue that such cases mainly occur if a defaulted contract with a rather low EAD yields a high recovery from the sale of the asset. Because we incorporate the workout expenses, LGDs greater than one are also feasible. Thus, we do not bound LGDs within the [0,1] interval, as is common for bank loans and as is done by Bastos (2010), by Calabrese and Zenga (2010), and by Loterman et al. (2012).
An LGD of 45%, as specified in the standard credit risk approach, is consider- ably higher than the median LGDs observed for companies B and C. In general, we emphasize that the shape of the LGD distribution varies significantly among these three companies. As presented in Figure 2.1, only the LGD distribution of company C exhibits the frequently mentioned bimodal shape, whereas those of companies A and B feature three maxima. These differences continue to prevail when we account for differences in the leasing portfolio. Thus, we trace these vari- ations back to differences in workout policies. Because the requirements for the pooling of LGD data, set out in section 456 of the Basel II accord, are clearly vio-
2.2 Dataset 17
–.5 0 .5 1 1.5
LGD
A B C
Figure 2.1: Density of the realized loss given default (LGD) by company. The realized LGD concentrates on the interval [−0.5,1.5]. The figures describe a loss severity of
−50% on the left end, which indicates that 150% of the exposure at default (EAD) was
recovered. On the right end, the loss severity is 150%, indicating a loss of 150% of the EAD. Consequently, a realized LGD of 0 or 1 indicates the following: in case of 0, full coverage of the EAD (included workout costs); or, in case of 1, total loss of the EAD.
lated, we construct individual estimation models to account for institution-specific characteristics and differences in LGD profiles among the companies.
Previous studies on the LGD of defaulted leasing contracts consistently show that the LGD distribution depends largely on the underlying asset type. We cat- egorize the contracts according to the underlying asset using five classes: vehicles, machinery, information and communications technology (ICT), equipment, and other. Table 2.3 summarizes the key statistical figures of the distributions for each company. We can unambiguously rank the three companies with respect to their mean LGD. Company B achieves the lowest average LGD for all asset types, company C is second best, and company A bears the highest losses. Contracts in ICT have the highest average LGD. Examining the median of ICT, we find that companies A, B, and C retrieve only 4%, 16%, and 13% of the EAD, respectively, in half of the cases. The key statistical figures for equipment and other assets are
Asset type Company # Contracts Mean Std Median Vehicles A 4,578 0 .44 0.35 0.45 B 1,111 0.26 0.31 0.27 C 599 0.28 0.37 0.21 Machinery A 4,140 0 .55 0.43 0.61 B 779 0.06 0.27 0.00 C 646 0.39 0.42 0.32 ICT A 606 0 .77 0.38 0.96 B 1,062 0.64 0.43 0.84 C 201 0.72 0.38 0.87 Equipment A 353 0 .61 0.44 0.74 B 26 0.26 0.44 0.09 C 26 0.38 0.41 0.15 Other A 58 0 .56 0.43 0.54 B 17 0.39 0.44 0.26 C 120 0.46 0.43 0.45
Table 2.3: Loss given default (LGD) density information by asset type for companies A–C. For each asset type, # Contracts is the number of contracts containing this type of asset, Mean is its mean, Std is its standard deviation, and Median is its median. ICT is information and communications technology. The displayed asset types vary in the numbers of their contracts and even further in the characteristics of their realized LGD.
seemingly less meaningful because of the small sample sizes for these classes, but the trends are consistent across all three companies.
Figure 2.2 presents the LGD distributions for vehicles, machinery, and ICT for each company. The shape of the LGD distributions differs tremendously with respect to the different asset types. Whereas for ICT, the LGD density in Fig- ure 2.2c is right-skewed toward high LGDs with only weak bimodality throughout all of the companies, the density of machinery runs partly the opposite direction. For machinery, in Figure 2.2b, we see a higher concentration around 0, but for company A, larger LGDs again outweigh this effect. The LGD for contracts with vehicles varies greatly from company to company. We observe a strong multi- modality for all of the companies with an additional peak at approximately 0.5, and most of the density lies in the lower LGD range.
2.3 Methods 19